Subgroups — C₂⁴×C₄²×C₃₁ #21519397

Order 7936.

24030 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₃₁	C₂	1	3	yes	maximal
2	C₂³×C₄²×C₃₁	C₂	1	60	yes	maximal, direct product factor
3	C₂⁶×C₃₁	C₂²	1	1	yes	characteristic
4	C₂⁴×C₄×C₃₁	C₄	1	96	yes	direct product factor
5	C₂⁴×C₄×C₃₁	C₂²	1	90	yes	—
6	C₂²×C₄²×C₃₁	C₂²	1	560	yes	direct product factor
7	C₂⁵×C₃₁	C₂×C₄	1	48	yes	—
8	C₂⁵×C₃₁	C₂³	1	15	yes	—
9	C₂³×C₄×C₃₁	C₂×C₄	1	1440	yes	direct product factor
10	C₂³×C₄×C₃₁	C₂³	1	420	yes	—
11	C₂×C₄²×C₃₁	C₂³	1	960	yes	direct product factor
12	C₂⁴×C₃₁	C₄²	1	256	yes	direct product factor
13	C₂⁴×C₃₁	C₂²×C₄	1	360	yes	—
14	C₂⁴×C₃₁	C₂⁴	1	35	yes	—
15	C₂²×C₄×C₃₁	C₂²×C₄	1	3360	yes	direct product factor
16	C₂²×C₄×C₃₁	C₂⁴	1	360	yes	—
17	C₄²×C₃₁	C₂⁴	1	256	yes	direct product factor
18	C₂⁴×C₄²	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₃₁	C₂×C₄²	1	960	yes	direct product factor
20	C₂³×C₃₁	C₂³×C₄	1	420	yes	—
21	C₂³×C₃₁	C₂⁵	1	15	yes	—
22	C₂×C₄×C₃₁	C₂³×C₄	1	1440	yes	direct product factor
23	C₂×C₄×C₃₁	C₂⁵	1	48	yes	—
24	C₂⁵×C₄	C₂×C₃₁	1	3	yes	—
25	C₂³×C₄²	C₂×C₃₁	1	60	yes	direct product factor
26	C₂²×C₃₁	C₂²×C₄²	1	560	yes	direct product factor
27	C₂²×C₃₁	C₂⁴×C₄	1	90	yes	—
28	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
29	C₄×C₃₁	C₂⁴×C₄	1	96	yes	direct product factor
30	C₂⁶	C₂²×C₃₁	1	1	yes	characteristic
31	C₂⁴×C₄	C₄×C₃₁	1	96	yes	direct product factor
32	C₂⁴×C₄	C₂²×C₃₁	1	90	yes	—
33	C₂²×C₄²	C₂²×C₃₁	1	560	yes	direct product factor
34	C₂×C₃₁	C₂³×C₄²	1	60	yes	direct product factor
35	C₂×C₃₁	C₂⁵×C₄	1	3	yes	—
36	C₂⁵	C₂×C₄×C₃₁	1	48	yes	—
37	C₂⁵	C₂³×C₃₁	1	15	yes	—
38	C₂³×C₄	C₂×C₄×C₃₁	1	1440	yes	direct product factor
39	C₂³×C₄	C₂³×C₃₁	1	420	yes	—
40	C₂×C₄²	C₂³×C₃₁	1	960	yes	direct product factor
41	C₃₁	C₂⁴×C₄²	1	1	yes	characteristic, direct product factor, Sylow
42	C₂⁴	C₄²×C₃₁	1	256	yes	direct product factor
43	C₂⁴	C₂²×C₄×C₃₁	1	360	yes	—
44	C₂⁴	C₂⁴×C₃₁	1	35	yes	—
45	C₂²×C₄	C₂²×C₄×C₃₁	1	3360	yes	direct product factor
46	C₂²×C₄	C₂⁴×C₃₁	1	360	yes	—
47	C₄²	C₂⁴×C₃₁	1	256	yes	direct product factor
48	C₂³	C₂×C₄²×C₃₁	1	960	yes	direct product factor
49	C₂³	C₂³×C₄×C₃₁	1	420	yes	—
50	C₂³	C₂⁵×C₃₁	1	15	yes	—
51	C₂×C₄	C₂³×C₄×C₃₁	1	1440	yes	direct product factor
52	C₂×C₄	C₂⁵×C₃₁	1	48	yes	—
53	C₂²	C₂²×C₄²×C₃₁	1	560	yes	direct product factor
54	C₂²	C₂⁴×C₄×C₃₁	1	90	yes	—
55	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
56	C₄	C₂⁴×C₄×C₃₁	1	96	yes	direct product factor
57	C₂	C₂³×C₄²×C₃₁	1	60	yes	direct product factor
58	C₂	C₂⁵×C₄×C₃₁	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂²	C₂⁶×C₃₁
socle	C₂⁶×C₃₁	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂³×C₄²×C₃₁	C₂	direct (N × H)
4. C₂⁴×C₄×C₃₁	C₄	direct (N × H)
6. C₂²×C₄²×C₃₁	C₂²	direct (N × H)
9. C₂³×C₄×C₃₁	C₂×C₄	direct (N × H)
11. C₂×C₄²×C₃₁	C₂³	direct (N × H)
12. C₂⁴×C₃₁	C₄²	direct (N × H)
15. C₂²×C₄×C₃₁	C₂²×C₄	direct (N × H)
17. C₄²×C₃₁	C₂⁴	direct (N × H)
18. C₂⁴×C₄²	C₃₁	direct (N × H)
19. C₂³×C₃₁	C₂×C₄²	direct (N × H)
22. C₂×C₄×C₃₁	C₂³×C₄	direct (N × H)
25. C₂³×C₄²	C₂×C₃₁	direct (N × H)
26. C₂²×C₃₁	C₂²×C₄²	direct (N × H)
29. C₄×C₃₁	C₂⁴×C₄	direct (N × H)
31. C₂⁴×C₄	C₄×C₃₁	direct (N × H)
33. C₂²×C₄²	C₂²×C₃₁	direct (N × H)
34. C₂×C₃₁	C₂³×C₄²	direct (N × H)
38. C₂³×C₄	C₂×C₄×C₃₁	direct (N × H)
40. C₂×C₄²	C₂³×C₃₁	direct (N × H)
41. C₃₁	C₂⁴×C₄²	direct (N × H)
42. C₂⁴	C₄²×C₃₁	direct (N × H)
45. C₂²×C₄	C₂²×C₄×C₃₁	direct (N × H)
47. C₄²	C₂⁴×C₃₁	direct (N × H)
48. C₂³	C₂×C₄²×C₃₁	direct (N × H)
51. C₂×C₄	C₂³×C₄×C₃₁	direct (N × H)
53. C₂²	C₂²×C₄²×C₃₁	direct (N × H)
56. C₄	C₂⁴×C₄×C₃₁	direct (N × H)
57. C₂	C₂³×C₄²×C₃₁	direct (N × H)

Subgroups — C24×C42×C31 #21519397

Conjugacy classes of subgroups

Complements

Subgroups — C₂⁴×C₄²×C₃₁ #21519397